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Home » But we already have $ c_2 = \frac79160 $ - SUpost

But we already have $ c_2 = \frac79160 $ - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 x + \frac{1}{x} = 2

📌 Multiplying both sides by $ x $:

📌 x^2 + 1 = 2x \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1

📌 So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow 4b = 0 \Rightarrow b = 0 $

📌 Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

📌 \frac{a^2}{a^2} = \boxed{1}

📌 Question: A polynomial $ f(x) $ satisfies $ f(x + 1) - f(x) = 6x + 4 $. Find the leading coefficient of $ f(x) $.

📌 Solution: Since the difference $ f(x+1) - f(x) $ is linear, $ f(x) $ must be a quadratic polynomial. Let $ f(x) = ax^2 + bx + c $. Then:

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